CN113221974B - Cross map matching incomplete multi-view clustering method and device - Google Patents

Abstract

The present application discloses a method and device for clustering incomplete multi-views with cross graph matching. The method includes: establishing a missing value filling model for incomplete multi-modal data, where the multi-modal data includes web page data or multimedia data; Cross-graph matching model for modal data; combined with the objective functions of the missing value filling model and the cross-graph matching model, a cross-graph matching incomplete multi-view clustering model is established; the cross-graph matching incomplete multi-view clustering model is decomposed into three sub-sections The problem includes optimizing the missing matrix E, solving the mapping space U and updating the connection matrix S; using an iterative algorithm to solve the three sub-problems until the three sub-problems converge, the optimal solution is obtained. While reducing the impact of missing data, the present application utilizes consistent and complementary information between modalities to improve the clustering effect.

Description

A method and device for multi-view clustering with incomplete cross graph matching

technical field

The present application relates to the technical field of image clustering, and in particular, to a method and device for multi-view clustering with incomplete cross-graph matching.

Background technique

In the era of big data, the types of data collection channels and feature extraction are becoming more and more diverse, so that the same object can be described from multiple data sources and features, resulting in multi-modal data. A hyperlink to this page is described; a multimedia segment data can be described by its video and audio signals simultaneously. In practical applications, due to the time-consuming and labor-intensive label collection, only a small amount of supervised information can often be collected. However, the multimodal semi-supervised clustering method can combine limited supervised information with a large amount of unsupervised information to learn, which greatly improves the clustering performance. class effect.

However, in practical applications, due to the temporary failure of the data collector or human error, the data of some modalities is missing, and incomplete multi-view data is often obtained. Most of the existing multimodal clustering algorithms are designed based on complete data, and cannot directly deal with incomplete multimodal data. Therefore, incomplete multimodal clustering emerges as the times require. The consistent and complementary information between states can improve the clustering effect.

SUMMARY OF THE INVENTION

Embodiments of the present application provide a method and apparatus for multi-view clustering with incomplete cross graph matching, so that the clustering effect can be improved by using consistent and complementary information between modalities while reducing the impact of missing data.

In view of this, a first aspect of the present application provides a multi-view clustering method for incomplete cross graph matching, the method comprising:

establishing a missing value filling model for incomplete multimodal data, where the multimodal data includes web page data or multimedia data;

Build a cross-graph matching model for incomplete multimodal data;

In combination with the objective function of the missing value filling model and the cross-graph matching model, a multi-view clustering model with incomplete cross-graph matching is established;

Decomposing the multi-view clustering model with incomplete cross graph matching into three sub-problems, including optimizing the missing matrix E, solving the mapping space U and updating the connection matrix S;

The three sub-problems are solved by an iterative algorithm until the three sub-problems converge, and an optimal solution is obtained.

Optionally, the objective function of the missing value filling model is:

反之为0；U^(v)∈R^dv×N，v＝1，2，...，m表示多模态数据的映射空间；λ₁＞0是权衡参数；

是G^(v)的拉普拉斯矩阵，特征相似性矩阵G^(v)∈R^dv×dv由互knn图构建。where X ^(v) is the incomplete modal data, X ^(v) ∈ R ^dv×N , d _v is the feature dimension of the vth mode, {E ⁽¹⁾ , E ⁽²⁾ ,... , E ^(m) } represents the missing data of multiple modalities, where E ^(v) ∈ R ^dv×nv , n _v is the number of missing samples of the v-th modality, (Nn _v ) is the actual v-th modality Number of samples; relation matrix W ^(v) ∈ R ^nv×N , if the ith node in E ⁽ v) is the jth node in X ^(v) , then

On the contrary, it is 0; U ^(v) ∈ R ^dv×N , v=1, 2, ..., m represents the mapping space of multimodal data; λ ₁ >0 is a trade-off parameter;

is the Laplacian matrix of G ^(v) , and the feature similarity matrix G ^(v) ∈ R ^dv×dv is constructed from the mutual knn graph.

Optionally, the objective function of the cross graph matching model is:

和

分别表示映射空间U的第i列和第j列；

表示连接矩阵S的中的元素，

行和为1；ε表示数据样本集合；S^(v)和S^(w)表示任意两个视角的连接图。In the formula, λ ₂ > 0 is a trade-off parameter;

and

Represent the i-th column and the j-th column of the mapping space U, respectively;

represents the elements in the connection matrix S,

The row sum is 1; ε represents the set of data samples; S ^(v) and S ^(w) represent the connection graph of any two views.

Optionally, the objective function of the cross graph matching incomplete multi-view clustering model is:

Optionally, the iterative algorithm is used to solve the three sub-problems until the three sub-problems converge, and an optimal solution is obtained, including:

Initialize the connection matrix S;

Fix the mapping space U ^(v) and the connection matrix S ^(v) , update the missing matrix E ^(v) ;

Fix the missing matrix E ^(v) and the connection matrix S ^(v) , update the mapping space U ^(v) ;

The missing matrix E ^(v) and the mapping space U ^(v) are fixed, and the objective equation of the connection matrix S ^(v) is solved by an iterative algorithm.

Optionally, the initialization connection matrix S includes:

定义为：in,

defined as:

为采用实际样本数据X^(v)∈R^dv×N-nv构建相似图

In the formula,

Build a similarity graph for taking real sample data X ^(v) ∈ R ^dv×N-nv

Optionally, the fixed mapping space U ^(v) and the connection matrix S ^(v) update the missing matrix E ^(v) , including:

Optionally, the fixed missing matrix E ^(v) and the connection matrix S ^(v) update the mapping space U ^(v) , including

Optionally, fix the missing matrix E ^(v) and the mapping space U ^(v) , and solve the objective equation of the connection matrix S ^(v) by an iterative algorithm, including:

表示两个节点

和

的距离，

和

表示同一个视角中的两个数据。In the formula,

represents two nodes

and

the distance,

and

Represents two data in the same view.

A second aspect of the present application provides an incomplete multi-view clustering apparatus for cross graph matching, the apparatus comprising:

a first establishment unit, configured to establish a missing value filling model for incomplete multimodal data, where the multimodal data includes web page data or multimedia data;

The second establishment unit is used to establish a cross-graph matching model of incomplete multimodal data;

a third establishment unit, configured to establish a multi-view clustering model with incomplete cross-graph matching in combination with the objective function of the missing value filling model and the cross-graph matching model;

a decomposition unit, configured to decompose the incomplete multi-view clustering model of cross graph matching into three sub-problems, including optimizing the missing matrix E, solving the mapping space U and updating the connection matrix S;

The solving unit is used for solving the three sub-problems by using an iterative algorithm until the three sub-problems converge to obtain an optimal solution.

As can be seen from the above technical solutions, the present application has the following advantages:

In the present application, a method and device for clustering incomplete multi-views with cross graph matching are provided. The method includes: establishing a missing value filling model for incomplete multi-modal data, where the multi-modal data includes web page data or multimedia data; Cross-graph matching model for complete multimodal data; combined with the objective functions of the missing value filling model and the cross-graph matching model, a cross-graph matching incomplete multi-view clustering model is established; the cross-graph matching incomplete multi-view clustering model is decomposed into Three sub-problems, including optimizing the missing matrix E, solving the mapping space U and updating the connection matrix S; using an iterative algorithm to solve the three sub-problems until the three sub-problems converge, the optimal solution is obtained.

In this application, missing data is used as an optimization amount, so that missing values satisfy the latent feature structure of the view, thereby reducing the impact of missing data on clustering. At the same time, the graph learning method is used to innovatively transform the possibly changing view representation into an invariant graph connection strength, and minimize the difference of pairwise connection graphs between different views to achieve the goal of view consensus, thereby effectively reducing missing data. At the same time, the consistent and complementary information between modalities is used to improve the clustering effect.

Description of drawings

FIG. 1 is a flow chart of a method in an embodiment of a method for multi-view clustering with incomplete cross graph matching according to the present application;

FIG. 2 is a device structure diagram of an embodiment of an incomplete multi-view clustering device for cross graph matching according to the present application;

FIG. 3 is an example flowchart of an incomplete multi-view clustering algorithm using cross graph matching in an embodiment of the present application.

Detailed ways

In order to make those skilled in the art better understand the solutions of the present application, the technical solutions in the embodiments of the present application will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present application. Obviously, the described embodiments are only It is a part of the embodiments of the present application, but not all of the embodiments. Based on the embodiments in the present application, all other embodiments obtained by those of ordinary skill in the art without creative efforts shall fall within the protection scope of the present application.

Please refer to FIG. 1. FIG. 1 is a method flowchart of an embodiment of an incomplete multi-view clustering method for cross graph matching according to the present application. As shown in FIG. 1, FIG. 1 includes:

101. Establish a missing value filling model for incomplete multimodal data, where the multimodal data includes web page data or multimedia data;

It should be noted that the multimodal data in this application may include web page data or multimedia data, etc. For example, a web page data can be described by text, and can also be described by a hyperlink pointing to the page; a multimedia segment data can be Described by its video and audio signals simultaneously. This application is to perform clustering processing on this type of data.

Specifically, for a given multimodal data {X ⁽¹⁾ , X ⁽²⁾ , . . . , X ^(m) } with N samples and m modalities, where X ^(v) ∈ R ^{dv× N} , d _v are the feature dimensions of the vth modality, and the missing samples of each modality are denoted by 0. {E ⁽¹⁾ , E ⁽²⁾ ,...,E ^(m) } denotes missing data for multiple modalities, where E ^(v) ∈ R ^dv×nv , n _v is the missing of the vth modality Number of samples, (Nn _v ) is the actual number of samples for the vth mode.

In this application, the missing data {E ^(v) , v=1, 2, . That is, the semantic information hidden by the missing data is exploited. The missing value filling model is:

反之为0。where the missing values {E ^(v) , v=1, 2, . . . , m} can be initialized to the mean of the relevant modalities. The relation matrix W ^(v) ∈R ^nv×N , if the ith node in E ⁽ v) is the jth node in X ^(v) , then

Otherwise it is 0.

表示缺失矩阵的第i行，表示v模态下第i个特征，

表示特征i和特征j之间的相似度。公式中

的作用是，约束在实际样本条件下相似性强度大的任意两个特征，在缺失样本中其特征也相近。特征相似性矩阵G^(v)∈R^dv×dv由互knn图构建，计算方法是，如果不完整模态数据第v个模态的第i个特征是第j个特征的最相近的k个特征并且第j个特征是第i个特征的最相近的k个特征，那么

其具有鲁棒性。That is, E ^(v) W ^(v) can exactly correspond to the modal missing data, that is, it corresponds to the missing part shown in the left half of Figure 3. It can be seen from Figure 3 that X(v)+E ^(v) W ^(v) can be Represents the full modal information after filling.

represents the ith row of the missing matrix, which represents the ith feature in the v mode,

represents the similarity between feature i and feature j. formula

The function of is to constrain any two features with high similarity in actual sample conditions, and their features are also similar in missing samples. The feature similarity matrix G ^(v) ∈ R ^dv×dv is constructed from a mutual knn graph, calculated as if the ith feature of the vth modality of incomplete modal data is the k closest k of the jth feature feature and the j-th feature is the k-th closest feature to the i-th feature, then

It is robust.

可以简写成

其中

是G^(v)的拉普拉斯矩阵，因此，上式可以变形为：

can be abbreviated as

in

is the Laplace matrix of G ^(v) , so the above formula can be transformed into:

102. Establish a cross graph matching model for incomplete multimodal data;

和

也很相近。由于不同模态的表示不尽相同，为避免在实现共识目标的时候强制得到共同表示而导致失真的情况，将可能变化的视图表示转化为具有不变性的图连接强度。同样的，图学习需要考虑样本表示之间的关系，如果任意两个样本之间的表示

和

在v模态中相近，那么

应该也比较大。由此可见，表达性和连接性的学习是相互影响的一个过程。根据上述讨论，对每个模态构图为：It should be noted that {U ^(v) ∈ R ^dv×N , v=1, 2, . . . , m} may represent a multimodal mapping space. In this way, the original feature is used as an important basis for representation learning, U ^(v) should be close to X ^(v) , otherwise the topology will be destroyed. In addition, the similarity between each sample should also be considered: if two samples have high similarity in a modality, then their representation

and

Also very close. Since the representations of different modalities are not the same, in order to avoid the distortion caused by forcing a common representation to achieve the consensus goal, the view representation that may change is transformed into an invariant graph connection strength. Similarly, graph learning needs to consider the relationship between sample representations, if the representation between any two samples

and

close in the v-mode, then

Should be bigger too. Thus, expressive and connected learning is a process that influences each other. According to the above discussion, the composition for each modality is:

和

分别表示映射空间U的第i列和第j列；λ₁，λ₂＞0是权衡参数。另外，使用概率来衡量连接强度；

表示连接矩阵S的中的元素，

行和为1。in,

and

respectively represent the i-th column and the j-th column of the mapping space U; λ ₁ , λ ₂ >0 are trade-off parameters. Also, use probability to measure connection strength;

represents the elements in the connection matrix S,

The row sum is 1.

Like multi-view clustering, incomplete multi-view clustering still has two challenges to solve: 1) how to mine consistent information; 2) how to express the relationship between views. In this application, pairwise matching between multiple connection graphs constructed by constraining the mapping space, that is, minimizing the difference between any two connection graphs, and constructing a view consensus. Minimize differences between views:

That is, the objective function of the cross graph matching model is:

103. Combine the objective function of the missing value filling model and the cross-graph matching model to establish a multi-view clustering model with incomplete cross-graph matching;

104. Decompose the incomplete multi-view clustering model of cross graph matching into three sub-problems, including optimizing the missing matrix E, solving the mapping space U and updating the connection matrix S;

It should be noted that this application can decompose the multi-view clustering model with incomplete cross graph matching into three sub-problems, including optimizing the missing matrix E, solving the mapping space U, and updating the connection matrix S, respectively.

105. Use an iterative algorithm to solve the three sub-problems until the three sub-problems converge, and obtain the optimal solution.

It should be noted that this application can use an iterative algorithm to solve the three sub-problems until the three sub-problems converge, and obtain the optimal solution, including:

501. Initialize the connection matrix S;

初始化目标方程为：It should be noted that this application can first initialize the connection matrix S. Specifically, in order to reduce the influence of missing values on the composition, the similarity graph can be constructed using the actual sample data X ^(v) ∈ R ^dv×N-nv

The initialization objective equation is:

和

的距离

越近，相似度

越大，

和

表示同一个视角中的两个数据。第二项对

的L₂正则使得相似矩阵

稀疏。令k为最近邻居的个数，初始化

为：If two nodes

and

the distance

The closer, the similarity

the bigger the

and

Represents two data in the same view. second pair

The L ₂ regularity makes the similarity matrix

Sparse. Let k be the number of nearest neighbors, initialize

for:

进行转换操作：Since the complete view S ^(v) needs to be updated eventually, in order to obtain the complete view S ^(v) , for

To convert:

定义为：in,

defined as:

502. Fix the mapping space U ^(v) and the connection matrix S ^(v) , and update the missing matrix E ^(v) ;

It should be noted that the missing parts in the incomplete multimodal data matrix X ^(v) corresponding to the missing matrix E ^(v) are all 0, so the objective equation for updating E ^(v) can be changed to:

的偏导为：beg

The partial derivative is:

得到E^(v)的闭式解：make the deflection

Get the closed-form solution for E ^(v) :

503. Fix the missing matrix E ^(v) and the connection matrix S ^(v) , and update the mapping space U ^(v) ;

It should be noted that the objective equation for solving U ^(v) is:

是S^(v)的拉普拉斯矩阵。与求解E^(v)的方式类似，可以得到U^(v)的闭式解：in

is the Laplace matrix of S ^(v) . In a similar way to solving for E ^(v) , the closed-form solution for U ^(v) can be obtained:

504. Fix the missing matrix E(v) and the mapping space U(v), and solve the objective equation of the connection matrix S(v) through an iterative algorithm.

It should be noted that the objective equation for solving S ^(v) is:

上述公式可以改写为：make

The above formula can be rewritten as:

S ^(v) can be solved iteratively until the connection matrix converges S ^(v) .

In this application, missing data is used as an optimization amount, so that missing values satisfy the latent feature structure of the view, thereby reducing the impact of missing data on clustering. At the same time, the graph learning method is used to innovatively transform the possibly changing view representation into an invariant graph connection strength, and minimize the difference of pairwise connection graphs between different views to achieve the goal of view consensus, thereby effectively reducing missing data. At the same time, the consistent and complementary information between modalities is used to improve the clustering effect.

The above are the embodiments of the method of the present application, and the present application also provides an embodiment of an incomplete multi-view clustering apparatus for cross graph matching, as shown in FIG. 2 , which includes:

201. A first establishment unit, configured to establish a missing value filling model for incomplete multimodal data, where the multimodal data includes web page data or multimedia data;

202. A second establishment unit, configured to establish a cross-graph matching model of incomplete multimodal data;

203. A third establishment unit, configured to combine the objective function of the missing value filling model and the cross-graph matching model to establish a multi-view clustering model with incomplete cross-graph matching;

204. A decomposition unit, which is used to decompose the multi-view clustering model with incomplete cross-graph matching into three sub-problems, including optimizing the missing matrix E, solving the mapping space U and updating the connection matrix S;

205. A solving unit, used to solve the three sub-problems by using an iterative algorithm until the three sub-problems converge, and obtain an optimal solution.

Those skilled in the art can clearly understand that, for the convenience and brevity of description, the specific working process of the system, device and unit described above may refer to the corresponding process in the foregoing method embodiments, which will not be repeated here.

The terms "first", "second", "third", "fourth", etc. in the description of the present application and the above-mentioned drawings are used to distinguish similar objects, and are not necessarily used to describe a specific order or sequence. . It is to be understood that data so used may be interchanged under appropriate circumstances such that the embodiments of the application described herein can, for example, be practiced in sequences other than those illustrated or described herein. Furthermore, the terms "comprising" and "having", and any variations thereof, are intended to cover non-exclusive inclusion, for example, a process, method, system, product or device comprising a series of steps or units is not necessarily limited to those expressly listed Rather, those steps or units may include other steps or units not expressly listed or inherent to these processes, methods, products or devices.

It should be understood that, in this application, "at least one (item)" refers to one or more, and "a plurality" refers to two or more. "And/or" is used to describe the relationship between related objects, indicating that there can be three kinds of relationships, for example, "A and/or B" can mean: only A, only B, and both A and B exist , where A and B can be singular or plural. The character "/" generally indicates that the associated objects are an "or" relationship. "At least one item(s) below" or similar expressions thereof refer to any combination of these items, including any combination of single item(s) or plural items(s). For example, at least one (a) of a, b or c, can mean: a, b, c, "a and b", "a and c", "b and c", or "a and b and c" ", where a, b, c can be single or multiple.

In the several embodiments provided in this application, it should be understood that the disclosed system, apparatus and method may be implemented in other manners. For example, the apparatus embodiments described above are only illustrative. For example, the division of the units is only a logical function division. In actual implementation, there may be other division methods. For example, multiple units or components may be combined or Can be integrated into another system, or some features can be ignored, or not implemented. On the other hand, the shown or discussed mutual coupling or direct coupling or communication connection may be through some interfaces, indirect coupling or communication connection of devices or units, and may be in electrical, mechanical or other forms.

The units described as separate components may or may not be physically separated, and components displayed as units may or may not be physical units, that is, may be located in one place, or may be distributed to multiple network units. Some or all of the units may be selected according to actual needs to achieve the purpose of the solution in this embodiment.

In addition, each functional unit in each embodiment of the present application may be integrated into one processing unit, or each unit may exist physically alone, or two or more units may be integrated into one unit. The above-mentioned integrated units may be implemented in the form of hardware, or may be implemented in the form of software functional units.

As mentioned above, the above embodiments are only used to illustrate the technical solutions of the present application, but not to limit them; although the present application has been described in detail with reference to the foregoing embodiments, those of ordinary skill in the art should understand: The technical solutions described in the embodiments are modified, or some technical features thereof are equivalently replaced; and these modifications or replacements do not make the essence of the corresponding technical solutions deviate from the spirit and scope of the technical solutions in the embodiments of the present application.

Claims (6)

1. A cross map matching incomplete multi-view clustering method is characterized by comprising the following steps:

establishing a missing value filling model of incomplete multi-modal data, wherein the multi-modal data comprises webpage data or multimedia data;

the semantic information hidden by the missing data is utilized, the missing data is regarded as an optimizable variable, so that the missing data is clustered and optimized and updated according to the characteristic distribution under each mode, and the objective function of the missing value filling model is as follows:

in the formula, X^(v)For incomplete modal data, X^(v)∈R^dv×N，d_vIs the characteristic dimension of the v-th modality, { E⁽¹⁾，E⁽²⁾，...，E^(m)Denotes missing data of multiple modalities, where E^(v)∈R^dv×nv，n_vIs the number of missing samples for the v-th mode, (N-N)_v) Is the number of actual samples of the v-th mode; relationship matrix W^(v)∈R^nv×NIf E is^(v)Wherein the ith node is X^(v)J (th) node in, then

Otherwise, the value is 0; u shape^(v)∈R^dv×NV 1, 2.. m denotes a mapping space of the multi-modal data; lambda [ alpha ]₁>0 is a trade-off parameter;

is G^(v)Laplacian matrix of, feature similarity matrix G^(v)∈R^dv×dvConstructed from a mutual knn graph

Establishing a cross map matching model of incomplete multi-modal data; wherein the view representation of possible changes is converted into a graph connection strength with invariance; specifically, a plurality of connection graphs constructed through a constraint mapping space are matched pairwise, and view consensus is constructed; the target function of the cross map matching model is as follows:

in the formula, λ₂>0 is a trade-off parameter;

and

an ith column and a jth column respectively representing the mapping space U;

representing the elements in the connection matrix S,

the row is 1; epsilon represents a set of data samples; s^(v)And S^(w)A connection diagram representing any two perspectives;

combining the missing value filling model and the target function of the cross map matching model to establish a cross map matching incomplete multi-view clustering model; wherein the objective function of the cross map matching incomplete multi-view clustering model is as follows:

decomposing the incomplete cross map matching multi-view clustering model into three sub-problems, including optimizing a missing matrix E, solving a mapping space U and updating a connection matrix S;

solving the three subproblems by adopting an iterative algorithm until the three subproblems are converged to obtain an optimal solution, wherein the optimal solution comprises the following steps:

initializing a connection matrix S; in order to reduce the influence of missing values on the composition, constructing a similar graph by adopting actual sample data;

fixed mapping space U^(v)And a connection matrix S^(v)Update the missing matrix E^(v)；

Fixed miss matrix E^(v)And a connection matrix S^(v)Updating the mapping space U^(v)；

Fixed miss matrix E^(v)And a mapping space U^(v)Solving the connection matrix S by an iterative algorithm^(v)The target equation of (1).

2. The cross-map matching incomplete multi-view clustering method according to claim 1, wherein the initializing the connection matrix S comprises:

wherein,

is defined as:

in the formula,

to adopt actual sample data X^(v)∈R^dv×N-nvConstructing a similar graph

3. The method of claim 1The cross map matching incomplete multi-view clustering method is characterized in that the fixed mapping space U^(v)And a connection matrix S^(v)Update the missing matrix E^(v)The method comprises the following steps:

4. the cross-map matching incomplete multi-view clustering method of claim 1, wherein the fixed missing matrix E^(v)And a connection matrix S^(v)Updating the mapping space U^(v)Comprises that

In the formula,

is the laplace matrix of s (v).

5. The cross-map matching incomplete multi-view clustering method of claim 1, characterized in that the missing matrix E is fixed^(v)And a mapping space U^(v)Solving the connection matrix S by an iterative algorithm^(v)The target equation of (1), comprising:

in the formula,

to representTwo nodes

And

the distance of (a) to (b),

and

representing two data in the same view.

6. A cross-map matching incomplete multi-view clustering device, comprising:

the system comprises a first establishing unit, a second establishing unit and a third establishing unit, wherein the first establishing unit is used for establishing a missing value filling model of incomplete multi-modal data, and the multi-modal data comprises webpage data or multimedia data;

the semantic information hidden by the missing data is utilized, the missing data is regarded as an optimizable variable, so that the missing data is clustered and optimized and updated according to the characteristic distribution under each mode, and the objective function of the missing value filling model is as follows:

in the formula, X^(v)For incomplete modal data, X^(v)∈R^dv×N，d_vIs the characteristic dimension of the v-th modality, { E⁽¹⁾，E⁽²⁾，...，E^(m)Denotes missing data of multiple modalities, where E^(v)∈R^dv×nv，n_vIs the number of missing samples for the v-th mode, (N-N)_v) Is the number of actual samples of the v-th mode; relationship matrix W^(v)∈R^nv×NIf E is^(v)Wherein the ith node is X^(v)J (th) node in, then

Otherwise, the value is 0; u shape^(v)∈R^dv×NV 1, 2.. m denotes a mapping space of the multi-modal data; lambda [ alpha ]₁>0 is a trade-off parameter;

is G^(v)Laplacian matrix of, feature similarity matrix G^(v)∈R^dv×dvConstructed from a mutual knn graph

The second establishing unit is used for establishing a cross map matching model of incomplete multi-modal data;

wherein the view representation of possible changes is converted into a graph connection strength with invariance; specifically, a plurality of connection graphs constructed through a constraint mapping space are matched pairwise, and view consensus is constructed; the target function of the cross map matching model is as follows:

in the formula, λ₂>0 is a trade-off parameter;

and

an ith column and a jth column respectively representing the mapping space U;

representing a connection matrixThe elements of S are selected from the group consisting of,

the row is 1; epsilon represents a set of data samples; s^(v)And S^(w)A connection diagram representing any two perspectives;

the third establishing unit is used for combining the missing value filling model and the target function of the cross map matching model to establish a cross map matching incomplete multi-view clustering model; wherein the objective function of the cross map matching incomplete multi-view clustering model is as follows:

the decomposition unit is used for decomposing the incomplete cross map matching multi-view clustering model into three sub-problems, including optimizing a missing matrix E, solving a mapping space U and updating a connection matrix S;

the solving unit is used for solving the three subproblems by adopting an iterative algorithm until the three subproblems are converged to obtain an optimal solution, and comprises the following steps:

initializing a connection matrix S; in order to reduce the influence of missing values on the composition, constructing a similar graph by adopting actual sample data;

fixed mapping space U^(v)And a connection matrix S^(v)Update the missing matrix E^(v)；

Fixed miss matrix E^(v)And a connection matrix S^(v)Updating the mapping space U^(v)；

Fixed miss matrix E^(v)And a mapping space U^(v)Solving the connection matrix S by an iterative algorithm^(v)The target equation of (1).

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